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Magnetic Effects of Electric Current - Describe magnetic field, field lines, and field due to current-carrying conductor or solenoid

Grade 10CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Magnetic field due to a circular loop: The magnetic field lines are concentric circles at every point of the current-carrying circular loop. At the center of the loop, these lines appear as straight lines.

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The magnetic field BB produced by a circular coil is directly proportional to the current II passing through it (B∝IB \propto I) and inversely proportional to the radius rr of the loop (B∝1rB \propto \frac{1}{r}).

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If there is a coil having nn turns, the field produced is nn times as large as that produced by a single turn, because the current in each circular turn has the same direction and the fields due to each turn add up.

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Solenoid: A coil of many circular turns of insulated copper wire wrapped closely in the shape of a cylinder is called a solenoid.

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The magnetic field pattern of a solenoid is similar to that of a bar magnet. One end of the solenoid behaves as a magnetic North pole, while the other behaves as a South pole.

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Magnetic field inside a solenoid: The field lines inside the solenoid are in the form of parallel straight lines. This indicates that the magnetic field is uniform at all points inside the solenoid.

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Electromagnet: A strong magnetic field produced inside a solenoid can be used to magnetize a piece of magnetic material, like soft iron, when placed inside the coil. The magnet so formed is called an electromagnet.

📐Formulae

B∝IB \propto I

B∝nB \propto n

B∝1r (for a circular loop)B \propto \frac{1}{r} \text{ (for a circular loop)}

B=μ0nI (for an ideal solenoid)B = \mu_0 n I \text{ (for an ideal solenoid)}

💡Examples

Problem 1:

A circular coil of 100100 turns has a radius of 10 cm10 \text{ cm} and carries a current of 5 A5 \text{ A}. If the number of turns is doubled to 200200 and the current remains the same, how does the magnetic field at the center change?

Solution:

The magnetic field BB at the center of a circular coil is directly proportional to the number of turns nn. Since B∝nB \propto n, if nn increases from 100100 to 200200 (doubled), the magnetic field BB will also double.

Explanation:

In a coil with nn turns, the magnetic field produced by each turn adds up because the current flows in the same direction in all turns. Thus, Bnew=2×BoldB_{new} = 2 \times B_{old}.

Problem 2:

Identify the nature of the magnetic field inside a long current-carrying solenoid. If a soft iron core is inserted, what happens to the field strength?

Solution:

The magnetic field inside a long solenoid consists of parallel straight lines, indicating a uniform magnetic field. Inserting a soft iron core significantly increases the magnetic field strength, forming an electromagnet.

Explanation:

Soft iron has high permeability, which concentrates the magnetic field lines, thereby increasing the total magnetic induction BB inside the solenoid.